Components of Market Risk and Return

This article proposes a flexible but parsimonious specification of the joint dynamics of market risk and return to produce forecasts of a time-varying market equity premium. Our parsimonious volatility model allows components to decay at different rates, generates mean-reverting forecasts, and allows variance targeting. These features contribute to realistic equity premium forecasts for the U.S. market over the 1840–2006 period. For example, the premium forecast was low in the mid-1990s but has recently increased. Although the market's total conditional variance has a positive effect on returns, the smooth long-run component of volatility is more important for capturing the dynamics of the premium. This result is robust to univariate specifications that condition on either levels or logs of past realized volatility (RV), as well as to a new bivariate model of returns and RV.